Comment on "T-dependence of the magnetic penetration depth in unconventional superconductors at low temperatures: Can it be linear?"

We show that the clean superconductor with line of gap nodes is not in conflict with the Nernst theorem. The answer to the question in the title of the Schopohl-Dolgov paper in Phys. Rev. Lett. 80 (1998) 4761 (cond-mat/9802264) is yes.Comment: Comment to the paper by Schopohl and Dolgov in Phys. Rev. Lett. 80 (1998) 4761 (cond-mat/9802264), RevTex file, 1 page, no figures, typos are corrected, submitted to Phys. Rev. Let

Low temperature thermal conductivity in a d-wave superconductor with coexisting charge order: Effect of self-consistent disorder and vertex corrections

Given the experimental evidence of charge order in the underdoped cuprate superconductors, we consider the effect of coexisting charge order on low-temperature thermal transport in a d-wave superconductor. Using a phenomenological Hamiltonian that describes a two-dimensional system in the presence of a Q=(\pi,0) charge density wave and d-wave superconducting order, and including the effects of weak impurity scattering, we compute the self-energy of the quasiparticles within the self-consistent Born approximation, and calculate the zero-temperature thermal conductivity using linear response formalism. We find that vertex corrections within the ladder approximation do not significantly modify the bare-bubble result that was previously calculated. However, self-consistent treatment of the disorder does modify the charge-order-dependence of the thermal conductivity tensor, in that the magnitude of charge order required for the system to become effectively gapped is renormalized, generally to a smaller value.Comment: 19 pages, 15 figure

Superfluid density and competing orders in d-wave superconductors

We derive expressions for the superfluid density $\rho_s$ in the low-temperature limit $T \to 0$ in d-wave superconductors, taking into account the presence of competing orders such as spin-density waves, $i d_{xy}$-pairing, etc. Recent experimental data for the thermal conductivity and for elastic neutron scattering in La$_{2-x}$Sr$_x$CuO$_4$ suggest there are magnetic field induced anomalies that can be interpreted in terms of competing orders. We consider the implications of these results for the superfluid density and show in the case of competing spin-density wave order that the usual Volovik-like $\sqrt{H}$ depletion of $\rho_s(H)$ is replaced by a slower dependence on applied magnetic field. We find that it is crucial to include the competing order parameter in the self-consistent equation for the impurity scattering rate.Comment: 17 pages, RevTeX4, 6 EPS figures; final version published in PR

Free Energy and Magnetic Penetration Depth of a dd-Wave Superconductor in the Meissner State

We investigate the free energy and the penetration depth of a quasi-two-dimensional d-wave superconductor in the presence of a weak magnetic field by taking account of thermal, nonlocal and nonlinear effects. In an approximation in which the superfluid velocity $v_s$ is assumed to be slowly varying, the free energy is calculated and compared with available results in several limiting cases. It is shown that either nonlocal or nonlinear effects may cut off the linear-$T$ dependence of both the free energy and the penetration depth in all the experimental geometries. At extremely low $T$, the nonlocal effects will also generically modify the linear $H$ dependence of the penetration depth ("nonlinear Meissner effect") in most experimental geometries, but for supercurrents oriented along the nodal directions, the effect may be recovered. We compare our predictions with existing experiments on the cuprate superconductors.Comment: 18 revtex pages with 4 eps figures, final versio

Vortex in a d-wave superconductor at low temperatures

A systematic perturbation theory is developed to describe the magnetic field-induced subdominant $s$- and $d_{xy}$-wave order parameters in the mixed state of a $d_{x^2-y^2}$-wave superconductor, enabling us to obtain, within weak-coupling BCS theory, analytic results for the free energy of a d-wave superconductor in an applied magnetic field H_{c1}\ltsim H\ll H_{c2} from $T_c$ down to very low temperatures. Known results for a single isolated vortex in the Ginzburg-Landau regime are recovered, and the behavior at low temperatures for the subdominant component is shown to be qualitatively different. In the case of subdominant $d_{xy}$ pair component, superfluid velocity gradients and an orbital Zeeman effect are shown to compete in determining the vortex state, but for realistic field strengths the latter appears to be irrelevant. On this basis, we argue that recent predictions of a low-temperature phase transition in connection with recent thermal conductivity measurements are unlikely to be correct.Comment: 20 RevTEX pages, 6 EPS figures; considerably expanded versio

Absence of non-linear Meissner effect in YBa2Cu3O6.95

We present measurements the field and temperature dependence of the penetration depth (lambda) in high purity, untwinned single crystals of YBa2Cu3O6.95 in all three crystallographic directions. The temperature dependence of lambda is linear down to low temperatures, showing that our crystals are extremely clean. Both the magnitude and temperature dependence of the field dependent correction to lambda however, are considerably different from that predicted from the theory of the non-linear Meissner effect for a d-wave superconductor (Yip-Sauls theory). Our results suggest that the Yip-Sauls effect is either absent or is unobservably small in the Meissner state of YBa2Cu3O6.95.Comment: 4 pages, 4 figures (Latex file + Postscipt figures

Validation of the Chinese version of the "Mood Disorder Questionnaire" for screening bipolar disorder among patients with a current depressive episode

<p>Abstract</p> <p>Background</p> <p>The Mood Disorder Questionnaire (MDQ) is a well-recognized screening tool for bipolar disorder, but its Chinese version needs further validation. This study aims to measure the accuracy of the Chinese version of the MDQ as a screening instrument for bipolar disorder (BPD) in a group of patients with a current major depressive episode.</p> <p>Methods</p> <p>142 consecutive patients with an initial DSM-IV-TR diagnosis of a major depressive episode were screened for BPD using the Chinese translation of the MDQ and followed up for one year. The final diagnosis, determined by a special committee consisting of three trained senior psychiatrists, was used as a 'gold standard' and ROC was plotted to evaluate the performance of the MDQ. The optimal cut-off was chosen by maximizing the Younden's index.</p> <p>Results</p> <p>Of the 142 patients, 122 (85.9%) finished the one year follow-up. On the basis of a semi-structured clinical interview 48.4% (59/122) received a diagnosis of unipolar depression (UPD), 36.9% (45/122) BPDII and 14.8% (18/122) BPDI. At the end of the one year follow-up,9 moved from UPD to BPD, 2 from BPDII to UPD, 1 from BPDII to BPDI, the overall rate of initial misdiagnosis was 16.4%. MDQ showed a good accuracy for BPD: the optimal cut-off was 4, with a sensitivity of 0.72 and a specificity of 0.73. When BPDII and BPDI were calculated independently, the optimal cut-off for BPDII was 4, with a sensitivity of 0.70 and a specificity of 0.73; while the optimal cut-off for BPDI was 5, with a sensitivity of 0.67 and a specificity of 0.86.</p> <p>Conclusions</p> <p>Our results show that the Chinese version of MDQ is a valid tool for screening BPD in a group of patients with current depressive episode on the Chinese mainland.</p

Theory of c-axis Josephson tunneling in d-wave superconductors

The temperature and angular dependence of the c-axis Josephson current and the superfluid density in layered d-wave superconductors are studied within the framework of an extended Ambegaokar-Baratoff formalism. In particular, the effects of angle-dependent tunneling matrix elements and Andreev scattering at grain boundaries are taken into account. These lead to strong corrections of the low-temperature behavior of the plasma frequency and the Josephson current. Recent c-axis measurements on the cuprate high-temperature superconductors HgBa_2CaCu_{1+\delta} and Bi_2Sr_2CaCu_2O_{8+\delta} can therefore be interpreted to be consistent with a d-wave order parameter.Comment: Revtex, 4 pages with 4 eps figures, to appear in PRB R